Split mesh along Bezier curve in Blender 2.75
You have to just select the face you want to add a cut in and Subdivide it, by going (w) and the first option 'subdivide', then for instance you want a vertical cut, so select the horizontal edge and by pressing (x) or (Delete) key and choosing 'Dissolve Edges' you will delete it but with out corrupting the mesh, and then you can use the 'Edge Slide' to position your cut on any position on your face you want. To Edge Slide press  (Ctrl+E) and choose the fifth option from the bottom 'Edge Slide'.